I was listening to NPR this morning about the growing income gap between rich and middle class and it got me thinking about how people's incomes would be distributed in a simple, perfect world, where everyone starts with the same income and their income has an equal chance of increasing or decreasing a certain percentage every year. The fact that incomes are bounded below by 0 and not bounded above indicates that there will be a steadily increasing "tail" of ever-more wealthy individuals who represent less and less of the population, thereby increasing the income gap even though there is, by construction, no bias or favortism in the system. The income distribution would follow a version of Geometric Brownian Motion without drift.
Now, I know that this model is nowhere close to a realistic economic model; however, it serves to point out that income inequality can arise even without favortism for a subset of the population. I am not saying that this is the case, just that inequality is not required.
Therefore, why is there so much concern about the income gap as opposed to simply the income level/purchasing power of lower and middle income citizens?
Is there some ideal level of inequality in a healthy economy?